Theorem 19 ([1]})theorem]thm: general lb framework
Fix a function \(f:\left\lbrace 0,1\right\rbrace ^K\times \left\lbrace 0,1\right\rbrace ^K\rightarrow \left\lbrace \mathrm {true},\mathrm {false}\right\rbrace \)  and a graph predicate \(P\) . If there is a family \(\lbrace G_{x,y}\rbrace \)  of lower bound graphs for the \(\mathsf {CONGEST}\)  model w.r.t. \(f\)  and \(P\)  with cut edge set \(C = E(V_A, V_B)\) , then any deterministic algorithm for deciding \(P\)  in the \(\mathsf {CONGEST}\)  model requires \(\Omega (CC(f)/|C|\log n)\)  rounds, and any randomized algorithm for deciding \(P\)  in the \(\mathsf {CONGEST}\)  model requires \(\Omega (CC^R(f)/|C|\log n)\)  rounds.

